The structure of linear zero product and commutativity preservers of %$C^*%$-algebras
Abstract Let %$\theta :\mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) %$C^*%$-algebras. Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Liu, Jung-Hui [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales - Heidelberg [u.a.] : Springer, 2001, 115(2021), 4 vom: 17. Sept. |
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| Übergeordnetes Werk: |
volume:115 ; year:2021 ; number:4 ; day:17 ; month:09 |
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| DOI / URN: |
10.1007/s13398-021-01134-z |
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| Katalog-ID: |
SPR045102104 |
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| 100 | 1 | |a Liu, Jung-Hui |e verfasserin |4 aut | |
| 245 | 1 | 4 | |a The structure of linear zero product and commutativity preservers of %$C^*%$-algebras |
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| 520 | |a Abstract Let %$\theta :\mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) %$C^*%$-algebras. Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta (b)=\theta (b)\theta (a)%$). We show that %$\theta %$ is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of %$\mathcal {B}%$, and a real linear Jordan isomorphism %$J: \mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ such that %$\theta = hJ%$. | ||
| 650 | 4 | |a Zero product preservers |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Commutativity preservers |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Automatic continuity |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -algebras |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Li, Lei |0 (orcid)0000-0003-1177-7539 |4 aut | |
| 700 | 1 | |a Shi, Luoyi |4 aut | |
| 700 | 1 | |a Wong, Ngai-Ching |0 (orcid)0000-0002-1445-5335 |4 aut | |
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| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s13398-021-01134-z |z lizenzpflichtig |3 Volltext |
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10.1007/s13398-021-01134-z doi (DE-627)SPR045102104 (SPR)s13398-021-01134-z-e DE-627 ger DE-627 rakwb eng Liu, Jung-Hui verfasserin aut The structure of linear zero product and commutativity preservers of %$C^*%$-algebras 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021 Abstract Let %$\theta :\mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) %$C^*%$-algebras. Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta (b)=\theta (b)\theta (a)%$). We show that %$\theta %$ is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of %$\mathcal {B}%$, and a real linear Jordan isomorphism %$J: \mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ such that %$\theta = hJ%$. Zero product preservers (dpeaa)DE-He213 Commutativity preservers (dpeaa)DE-He213 Automatic continuity (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Li, Lei (orcid)0000-0003-1177-7539 aut Shi, Luoyi aut Wong, Ngai-Ching (orcid)0000-0002-1445-5335 aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 115(2021), 4 vom: 17. Sept. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:115 year:2021 number:4 day:17 month:09 https://dx.doi.org/10.1007/s13398-021-01134-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 115 2021 4 17 09 |
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10.1007/s13398-021-01134-z doi (DE-627)SPR045102104 (SPR)s13398-021-01134-z-e DE-627 ger DE-627 rakwb eng Liu, Jung-Hui verfasserin aut The structure of linear zero product and commutativity preservers of %$C^*%$-algebras 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021 Abstract Let %$\theta :\mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) %$C^*%$-algebras. Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta (b)=\theta (b)\theta (a)%$). We show that %$\theta %$ is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of %$\mathcal {B}%$, and a real linear Jordan isomorphism %$J: \mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ such that %$\theta = hJ%$. Zero product preservers (dpeaa)DE-He213 Commutativity preservers (dpeaa)DE-He213 Automatic continuity (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Li, Lei (orcid)0000-0003-1177-7539 aut Shi, Luoyi aut Wong, Ngai-Ching (orcid)0000-0002-1445-5335 aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 115(2021), 4 vom: 17. Sept. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:115 year:2021 number:4 day:17 month:09 https://dx.doi.org/10.1007/s13398-021-01134-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 115 2021 4 17 09 |
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10.1007/s13398-021-01134-z doi (DE-627)SPR045102104 (SPR)s13398-021-01134-z-e DE-627 ger DE-627 rakwb eng Liu, Jung-Hui verfasserin aut The structure of linear zero product and commutativity preservers of %$C^*%$-algebras 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021 Abstract Let %$\theta :\mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) %$C^*%$-algebras. Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta (b)=\theta (b)\theta (a)%$). We show that %$\theta %$ is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of %$\mathcal {B}%$, and a real linear Jordan isomorphism %$J: \mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ such that %$\theta = hJ%$. Zero product preservers (dpeaa)DE-He213 Commutativity preservers (dpeaa)DE-He213 Automatic continuity (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Li, Lei (orcid)0000-0003-1177-7539 aut Shi, Luoyi aut Wong, Ngai-Ching (orcid)0000-0002-1445-5335 aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 115(2021), 4 vom: 17. Sept. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:115 year:2021 number:4 day:17 month:09 https://dx.doi.org/10.1007/s13398-021-01134-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 115 2021 4 17 09 |
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10.1007/s13398-021-01134-z doi (DE-627)SPR045102104 (SPR)s13398-021-01134-z-e DE-627 ger DE-627 rakwb eng Liu, Jung-Hui verfasserin aut The structure of linear zero product and commutativity preservers of %$C^*%$-algebras 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021 Abstract Let %$\theta :\mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) %$C^*%$-algebras. Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta (b)=\theta (b)\theta (a)%$). We show that %$\theta %$ is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of %$\mathcal {B}%$, and a real linear Jordan isomorphism %$J: \mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ such that %$\theta = hJ%$. Zero product preservers (dpeaa)DE-He213 Commutativity preservers (dpeaa)DE-He213 Automatic continuity (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Li, Lei (orcid)0000-0003-1177-7539 aut Shi, Luoyi aut Wong, Ngai-Ching (orcid)0000-0002-1445-5335 aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 115(2021), 4 vom: 17. Sept. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:115 year:2021 number:4 day:17 month:09 https://dx.doi.org/10.1007/s13398-021-01134-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 115 2021 4 17 09 |
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10.1007/s13398-021-01134-z doi (DE-627)SPR045102104 (SPR)s13398-021-01134-z-e DE-627 ger DE-627 rakwb eng Liu, Jung-Hui verfasserin aut The structure of linear zero product and commutativity preservers of %$C^*%$-algebras 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021 Abstract Let %$\theta :\mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) %$C^*%$-algebras. Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta (b)=\theta (b)\theta (a)%$). We show that %$\theta %$ is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of %$\mathcal {B}%$, and a real linear Jordan isomorphism %$J: \mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ such that %$\theta = hJ%$. Zero product preservers (dpeaa)DE-He213 Commutativity preservers (dpeaa)DE-He213 Automatic continuity (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Li, Lei (orcid)0000-0003-1177-7539 aut Shi, Luoyi aut Wong, Ngai-Ching (orcid)0000-0002-1445-5335 aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 115(2021), 4 vom: 17. Sept. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:115 year:2021 number:4 day:17 month:09 https://dx.doi.org/10.1007/s13398-021-01134-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 115 2021 4 17 09 |
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Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 115(2021), 4 vom: 17. Sept. volume:115 year:2021 number:4 day:17 month:09 |
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Zero product preservers Commutativity preservers Automatic continuity -algebras |
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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales |
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Liu, Jung-Hui @@aut@@ Li, Lei @@aut@@ Shi, Luoyi @@aut@@ Wong, Ngai-Ching @@aut@@ |
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Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta (b)=\theta (b)\theta (a)%$). We show that %$\theta %$ is automatically continuous. 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| author |
Liu, Jung-Hui |
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Liu, Jung-Hui misc Zero product preservers misc Commutativity preservers misc Automatic continuity misc -algebras The structure of linear zero product and commutativity preservers of %$C^*%$-algebras |
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The structure of linear zero product and commutativity preservers of %$C^*%$-algebras Zero product preservers (dpeaa)DE-He213 Commutativity preservers (dpeaa)DE-He213 Automatic continuity (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 |
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misc Zero product preservers misc Commutativity preservers misc Automatic continuity misc -algebras |
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misc Zero product preservers misc Commutativity preservers misc Automatic continuity misc -algebras |
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misc Zero product preservers misc Commutativity preservers misc Automatic continuity misc -algebras |
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Elektronische Aufsätze Aufsätze Elektronische Ressource |
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The structure of linear zero product and commutativity preservers of %$C^*%$-algebras |
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| title_full |
The structure of linear zero product and commutativity preservers of %$C^*%$-algebras |
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Liu, Jung-Hui |
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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales |
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Liu, Jung-Hui Li, Lei Shi, Luoyi Wong, Ngai-Ching |
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Elektronische Aufsätze |
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Liu, Jung-Hui |
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10.1007/s13398-021-01134-z |
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| title_sort |
structure of linear zero product and commutativity preservers of %$c^*%$-algebras |
| title_auth |
The structure of linear zero product and commutativity preservers of %$C^*%$-algebras |
| abstract |
Abstract Let %$\theta :\mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) %$C^*%$-algebras. Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta (b)=\theta (b)\theta (a)%$). We show that %$\theta %$ is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of %$\mathcal {B}%$, and a real linear Jordan isomorphism %$J: \mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ such that %$\theta = hJ%$. © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021 |
| abstractGer |
Abstract Let %$\theta :\mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) %$C^*%$-algebras. Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta (b)=\theta (b)\theta (a)%$). We show that %$\theta %$ is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of %$\mathcal {B}%$, and a real linear Jordan isomorphism %$J: \mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ such that %$\theta = hJ%$. © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021 |
| abstract_unstemmed |
Abstract Let %$\theta :\mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) %$C^*%$-algebras. Suppose %$\theta %$ preserves commutativity in two directions (i.e., %$ab=ba%$ if and only if %$\theta (a)\theta (b)=\theta (b)\theta (a)%$). We show that %$\theta %$ is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of %$\mathcal {B}%$, and a real linear Jordan isomorphism %$J: \mathcal {A}_{sa}\rightarrow \mathcal {B}_{sa}%$ such that %$\theta = hJ%$. © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021 |
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The structure of linear zero product and commutativity preservers of %$C^*%$-algebras |
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https://dx.doi.org/10.1007/s13398-021-01134-z |
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Li, Lei Shi, Luoyi Wong, Ngai-Ching |
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| doi_str |
10.1007/s13398-021-01134-z |
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2024-07-03T13:47:40.242Z |
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